Martin QUINSON
École Normale Supérieure de Lyon, Laboratoire de l’Informatique du Parallélisme
Automatic discovery of the characteristics and capacities
- f a distributed computational platform
December 11th 2003
Automatic discovery of the characteristics and capacities of a - - PowerPoint PPT Presentation
Martin Q UINSON cole Normale Suprieure de Lyon, Laboratoire de lInformatique du Paralllisme Automatic discovery of the characteristics and capacities of a distributed computational platform December 11 th 2003 Introduction to the Grid
Martin QUINSON
École Normale Supérieure de Lyon, Laboratoire de l’Informatique du Parallélisme
December 11th 2003
Metacomputing: aggregating distributed computers and storage units the resulting platform is usually called the Grid
Share of local resources between several organizations ⇒ WAN constellation of LAN
Difficulties come from (amongst others):
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 2 / 27 ⊲⊲ |
Metacomputing: aggregating distributed computers and storage units the resulting platform is usually called the Grid
Share of local resources between several organizations ⇒ WAN constellation of LAN
Difficulties come from (amongst others):
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 2 / 27 ⊲⊲ |
Metacomputing: aggregating distributed computers and storage units the resulting platform is usually called the Grid
Share of local resources between several organizations ⇒ WAN constellation of LAN
Difficulties come from (amongst others):
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 2 / 27 ⊲⊲ |
Metacomputing: aggregating distributed computers and storage units the resulting platform is usually called the Grid
Share of local resources between several organizations ⇒ WAN constellation of LAN
Difficulties come from (amongst others):
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 2 / 27 ⊲⊲ |
Randomized scheduling:
Simple scheduling:
Current Grid scheduling:
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 3 / 27 ⊲⊲ |
Randomized scheduling:
Simple scheduling:
Current Grid scheduling:
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 3 / 27 ⊲⊲ |
NWS + FAST
ENV→ ALNeM
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 4 / 27 ⊲⊲ |
NWS + FAST
ENV→ ALNeM
Server Server Server Server Server Server Server Server Client Client Client Agent
Task2 Task1 Task3
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 4 / 27 ⊲⊲ |
NWS + FAST
ENV→ ALNeM
Server Server Server Server Server Server Server Server Client Client Client Network
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 4 / 27 ⊲⊲ |
NWS + FAST
ENV→ ALNeM
NWS [RSH99] forecasts:
Server Server Server Server Server Server Server Server Client
90Mo 97Mo 50Mo 534ko 42Mo 1Go 156Mo 1,3ko/s 2ko/s 280o/s 4,5Mo/s 1,7Go/s 23Mo/s 280o/s 60Mo/s
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 4 / 27 ⊲⊲ |
NWS + FAST
ENV→ ALNeM
NWS [RSH99] forecasts:
FAST [Qui02b] provides:
time and memory size (fitting to the host)
⇒ Duration of the task on each server
Server Server Server Server Server Server Server Server Client
1,3ko/s 2ko/s 280o/s 4,5Mo/s 1,7Go/s 23Mo/s 280o/s 534ko 90Mo 42Mo 97Mo 50Mo 156Mo 1Go 156Mo
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 4 / 27 ⊲⊲ |
NWS + FAST
ENV→ ALNeM Motivating example: how to configure NWS?
Server Server Server Server Server Server Server Server Client Client Client
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 4 / 27 ⊲⊲ |
NWS + FAST
ENV→ ALNeM Motivating example: how to configure NWS?
Server Server Server Server Server Server Server Server Client
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 4 / 27 ⊲⊲ |
NWS + FAST
ENV→ ALNeM Motivating example: how to configure NWS?
Target:
Server Server Server Server Server Server Server Server Client
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 4 / 27 ⊲⊲ |
NWS + FAST
ENV→ ALNeM
ENV [SBW99]:
Server Server Server Server Server Server Server Server Client
?
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 4 / 27 ⊲⊲ |
NWS + FAST
ENV→ ALNeM
ENV [SBW99]:
ALNeM [LQ04]
Server Server Server Server Server Server Server Server Client
?
166 32 42 5 6 1 8 10 16 101 103 20 105 106 109 22 11 12 14 19 110 112 114 39 118 119 121 124 34 126 36 13 15 130 131 133 134 31 136 138 46 60 141 143 144 40 146 147 148 4 7 152 153 154 47 155 158 159 44 18 75 161 164 58 165 167 168 169 17 80 170 171 172 173 174 52 175 176 177 179 59 70 180 182 183 53 2 27 3 51 21 25 28 85 23 24 29 26 30 35 33 37 38 9 45 41 50 54 55 56 57 61 62 63 64 66 67 68 69 71 72 73 74 76 78 79 86 92 94 96 98 99Martin QUINSON December 11th 2003 | ⊳⊳ Slide 4 / 27 ⊲⊲ |
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 4 / 27 ⊲⊲ |
Goal: (Grid) system availabilities measurement and forecasting
Leaded by Prof. Wolski (UCSB), used by AppLeS, Globus, NetSolve, Ninf, DIET, . . .
Architecture: Distributed system
Sensor: conducts the measurements Memory: stores the results Forecaster: forecasts statistically the tendencies Name server: directory service like LDAP
Memory Nameserver Sensor Sensor Forecaster
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 5 / 27 ⊲⊲ |
Goal: (Grid) system availabilities measurement and forecasting
Leaded by Prof. Wolski (UCSB), used by AppLeS, Globus, NetSolve, Ninf, DIET, . . .
Architecture: Distributed system
Sensor: conducts the measurements Memory: stores the results Forecaster: forecasts statistically the tendencies Name server: directory service like LDAP
Memory Nameserver Sensor Sensor Forecaster External source Test Test
Steady state: regular tests
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 5 / 27 ⊲⊲ |
Goal: (Grid) system availabilities measurement and forecasting
Leaded by Prof. Wolski (UCSB), used by AppLeS, Globus, NetSolve, Ninf, DIET, . . .
Architecture: Distributed system
Sensor: conducts the measurements Memory: stores the results Forecaster: forecasts statistically the tendencies Name server: directory service like LDAP
Request Client Memory Nameserver Sensor Sensor Forecaster
Handling of a request
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 5 / 27 ⊲⊲ |
Goal: (Grid) system availabilities measurement and forecasting
Leaded by Prof. Wolski (UCSB), used by AppLeS, Globus, NetSolve, Ninf, DIET, . . .
Architecture: Distributed system
Sensor: conducts the measurements Memory: stores the results Forecaster: forecasts statistically the tendencies Name server: directory service like LDAP
Client Memory Nameserver Sensor Sensor Forecaster
Handling of a request
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 5 / 27 ⊲⊲ |
Goal: (Grid) system availabilities measurement and forecasting
Leaded by Prof. Wolski (UCSB), used by AppLeS, Globus, NetSolve, Ninf, DIET, . . .
Architecture: Distributed system
Sensor: conducts the measurements Memory: stores the results Forecaster: forecasts statistically the tendencies Name server: directory service like LDAP
Answer Client Memory Nameserver Sensor Sensor Forecaster
Handling of a request
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 5 / 27 ⊲⊲ |
availableCpu (for an incoming process), currentCpu (for existing processes), bandwidthTcp, latencyTcp (Default: 64Kb in 16Kb messages; buffer=32Kb), connectTimeTcp, freeDisk, freeMemory, . . .
Data = serie: D1, D2, . . . , Dn−1, Dn. We want Dn+1. Methods are applied on D1, D2, . . . , Dn−1. each one predict Dn. Selection of the best on Dn to predict Dn+1.
Used statistical methods
mean: running, (adapting) sliding window ; median: idem ; gradian: GRAD(t, g) = (1−g)×GRAD(t−1, g) + g×value(t) ; last value.
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 6 / 27 ⊲⊲ |
NetPerf: HP project to sort network components, no interactivity GloPerf: Globus moves to NWS PingER: Regular pings between 600 hosts in 72 countries Iperf: Finds out the bandwidth by saturating the link for 30 seconds RPS: Forecasting limited to the CPU load Performance Co-Pilot (SGI):
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 7 / 27 ⊲⊲ |
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 7 / 27 ⊲⊲ |
Goals:
Architecture:
NWS FAST library
Needs modeling Sys availabilities
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 8 / 27 ⊲⊲ |
Goals:
Architecture:
LDAP Installation time Benchmarker NWS FAST library
Needs modeling Sys availabilities
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 8 / 27 ⊲⊲ |
Goals:
Architecture:
LDAP Runtime library Installation time Benchmarker Client application NWS FAST library
Needs modeling Sys availabilities
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 8 / 27 ⊲⊲ |
macro-benchmarking: benchmark {task; host} as a whole at installation
⇒ rather long, but only once
Structural decomposition by source analysis
No forecasting ⇒ selection of the fastest host Decomposition to extract simple parts Input of estimators from the application
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 9 / 27 ⊲⊲ |
macro-benchmarking: benchmark {task; host} as a whole at installation
⇒ rather long, but only once
Structural decomposition by source analysis
No forecasting ⇒ selection of the fastest host Decomposition to extract simple parts Input of estimators from the application
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 9 / 27 ⊲⊲ |
macro-benchmarking: benchmark {task; host} as a whole at installation
⇒ rather long, but only once
Structural decomposition by source analysis
No forecasting ⇒ selection of the fastest host Decomposition to extract simple parts Input of estimators from the application
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 9 / 27 ⊲⊲ |
macro-benchmarking: benchmark {task; host} as a whole at installation
⇒ rather long, but only once
Freddy [CDQF03], Structural decomposition by source analysis
integration underway
No forecasting ⇒ selection of the fastest host Decomposition to extract simple parts Input of estimators from the application
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 9 / 27 ⊲⊲ |
macro-benchmarking: benchmark {task; host} as a whole at installation
⇒ rather long, but only once
Freddy [CDQF03], Structural decomposition by source analysis
integration underway
No forecasting ⇒ selection of the fastest host Decomposition to extract simple parts Input of estimators from the application
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 9 / 27 ⊲⊲ |
dgeadd dgemm dtrsm icluster paraski icluster paraski icluster paraski Maximal 0.02s 0.02s 0.21s 5.8s 0.13s 0.31s error 6% 35% 0.3% 4% 10% 16% Average 0.006s 0.007s 0.025s 0.03s 0.02s 0.08s error 4% 6.5% 0.1% 0.1% 5% 7% dgeadd: Matrix addition dgemm: Matrix multiplication dtrsm: Triangular resolution icluster: bi-Pentium II, 256Mb, Linux, IMAG (Grenoble). paraski: Pentium III, 256Mb, Linux, IRISA (Rennes). network: Intra: LAN, 100Mb/s; Inter: VTHD network, 2.5Gb/s.
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 10 / 27 ⊲⊲ |
dgeadd dgemm dtrsm icluster paraski icluster paraski icluster paraski Maximal 0.02s 0.02s 0.21s 5.8s 0.13s 0.31s error 6% 35% 0.3% 4% 10% 16% Average 0.006s 0.007s 0.025s 0.03s 0.02s 0.08s error 4% 6.5% 0.1% 0.1% 5% 7% dgeadd: Matrix addition dgemm: Matrix multiplication dtrsm: Triangular resolution icluster: bi-Pentium II, 256Mb, Linux, IMAG (Grenoble). paraski: Pentium III, 256Mb, Linux, IRISA (Rennes). network: Intra: LAN, 100Mb/s; Inter: VTHD network, 2.5Gb/s.
Almost perfect: Maximal error < 1% ; Average error ≈ 0.1%
Code size + Matrix size (constant) (polynomial)
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 10 / 27 ⊲⊲ |
dgemm with background load (CPU-intensive process in background).
100 200 300 400 500 600 700 128 256 384 512 640 768 896 1024
Time (s) Matrices size Forecasted time on paraski Measured time on paraski Forecasted time on icluster Measured time on icluster
Maximal error: 22% Average error<10%
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 11 / 27 ⊲⊲ |
C =
Ci = Ar × Bi + Ai × Br
client/servers over LAN
20 40 60 80 100 120 140 160 128 256 384 512 640 768 896 1024
Time (s) Matrices size Measured time Forecasted time
Maximal error: 25%; Average error: 13%
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 12 / 27 ⊲⊲ |
100 200 300 400 500 600 700 128 256 384 512 640 768 896 1024
Time (s) Matrices size NetSolve forecast Measured time FAST forecast
Computation time of dgemm.
50 100 150 200 250 300 128 256 384 512 640 768 896 1024 1152
Time (s) Matrices size NetSolve forecast Measured time FAST forecast
Communication time of dgemm.
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 13 / 27 ⊲⊲ |
0.1 Time (s) µ (99569 s) µ (100685 s)
NWS FAST (cache miss)
µ (24 s)
FAST (cache hit)
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 14 / 27 ⊲⊲ |
Scheduler / NWS collaboration
Idle time Idle time Task run 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.5 1 1.5 2 2.5 3 3.5 Time (minutes) CPU availability (%)
Forecasting NWS: out of the box FAST: {sensors restart + forecaster reset} when the task starts or ends Theoretical value
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 15 / 27 ⊲⊲ |
NWS updated Task started Scheduling decision Task ended NWS updated
FAST asks NWS to update
NWS
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 16 / 27 ⊲⊲ |
Idle time Idle time Task running
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.5 1 1.5 2 2.5 3 3.5 Cpu availability (%) Time (minutes)
Measurements
Idle time Idle time Task running
0.5 1 1.5 2 2.5 3 3.5 Time (minutes) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Cpu availability (%)
Forecasting NWS: ADAPT_CPU FAST: ADAPT_CPU + virtual booking + sensors restart + forecaster reset Theoretical value (Result of 4 different runs)
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 17 / 27 ⊲⊲ |
20 40 60 80 100 120 140 160 128 256 384 512 640 768 896 1024
Time (s) Matrices size Measured time Forecasted time
Idle time Idle time Task running
0.5 1 1.5 2 2.5 3 3.5 Time (minutes) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Cpu availability (%)
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 18 / 27 ⊲⊲ |
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 18 / 27 ⊲⊲ |
Goal: Mapping the network topology Authors: Arnaud Legrand, Martin Quinson Motivation: Server hosting, Simulation, Collective Communication Forecasting Target application: NWS hosting Problem: Network experiments must not collide (Clique concept) Simplest: One big clique ; Better: Hierarchical
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 19 / 27 ⊲⊲ |
Goal: Mapping the network topology Authors: Arnaud Legrand, Martin Quinson Motivation: Server hosting, Simulation, Collective Communication Forecasting Target application: NWS hosting Problem: Network experiments must not collide (Clique concept) Simplest: One big clique ; Better: Hierarchical
Server Server Server Server Server Server Server Server Client Client Client
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 19 / 27 ⊲⊲ |
Goal: Mapping the network topology Authors: Arnaud Legrand, Martin Quinson Motivation: Server hosting, Simulation, Collective Communication Forecasting Target application: NWS hosting Problem: Network experiments must not collide (Clique concept) Simplest: One big clique ; Better: Hierarchical
Server Server Server Server Server Server Server Server Client
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 19 / 27 ⊲⊲ |
Goal: Mapping the network topology Authors: Arnaud Legrand, Martin Quinson Motivation: Server hosting, Simulation, Collective Communication Forecasting Focus: Discover interferences (limiting common links), not really packet paths
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 19 / 27 ⊲⊲ |
Goal: Mapping the network topology Authors: Arnaud Legrand, Martin Quinson Motivation: Server hosting, Simulation, Collective Communication Forecasting Focus: Discover interferences (limiting common links), not really packet paths
Method Restricted Focus Routers Notes SNMP authorized path all passive, dumb routers, LAN traceroute ICMP path all level 3 of OSI pathchar root path all link bandwidth, slow Other no path din = dout tree tomography bipartite [Rabbat03] ENV no interference some tree only
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 19 / 27 ⊲⊲ |
Def (non-interference): (ab) rl (cd) ⇐ ⇒
bwcd(ab) bw(ab)
≈ 1 Def (interference): (ab) rl (cd) ⇐ ⇒
bwcd(ab) bw(ab)
≈ 0.5 Def: Interference matrix I(V, rl) I(V, rl)(a, b, c, d) = 1 if (ab) rl (cd) if not INTERFERENCEGRAPH: Given H and I(H, rl), Find a graph G(V, E) and the associated routing satisfying: H ⊂ V I(H, G) = I(H, rl) |V | is minimal. .
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 20 / 27 ⊲⊲ |
Def (non-interference): (ab) rl (cd) ⇐ ⇒
bwcd(ab) bw(ab)
≈ 1 Def (interference): (ab) rl (cd) ⇐ ⇒
bwcd(ab) bw(ab)
≈ 0.5 Def: Interference matrix I(V, rl) I(V, rl)(a, b, c, d) = 1 if (ab) rl (cd) if not INTERFERENCEGRAPH: Given H and I(H, rl), Find a graph G(V, E) and the associated routing satisfying: H ⊂ V I(H, G) = I(H, rl) |V | is minimal. .
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 20 / 27 ⊲⊲ |
Def (non-interference): (ab) rl (cd) ⇐ ⇒
bwcd(ab) bw(ab)
≈ 1 Def (interference): (ab) rl (cd) ⇐ ⇒
bwcd(ab) bw(ab)
≈ 0.5 Def: Interference matrix I(V, rl) I(V, rl)(a, b, c, d) = 1 if (ab) rl (cd) if not INTERFERENCEGRAPH: Given H and I(H, rl), Find a graph G(V, E) and the associated routing satisfying: H ⊂ V I(H, G) = I(H, rl) |V | is minimal. .
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 20 / 27 ⊲⊲ |
⇒ ∀(u, v) ∈ H, (au) rl (bv) Lemma (separator): ∀a, b ∈ H, a ⊥ b ⇐ ⇒ ∃ ρ ∈ V
→ z)∩(b − → z) . (⊥⇐ ⇒ ∃ ρ separator) Theorem: ⊥ is an equivalence relation
(under some assumptions)
Theorem (representativity): C equivalence class under ⊥
(under some assumptions)
∀ρ, σ ∈ C, ∀b, u, v ∈ H, (ρ, u) rl (b, v) ⇔ (σ, u) rl (b, v) (you can interchange any member of the class by any other in the matrix)
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 21 / 27 ⊲⊲ |
⇒ ∀(u, v) ∈ H, (au) rl (bv) Lemma (separator): ∀a, b ∈ H, a ⊥ b ⇐ ⇒ ∃ ρ ∈ V
→ z)∩(b − → z) . (⊥⇐ ⇒ ∃ ρ separator) Theorem: ⊥ is an equivalence relation
(under some assumptions)
Theorem (representativity): C equivalence class under ⊥
(under some assumptions)
∀ρ, σ ∈ C, ∀b, u, v ∈ H, (ρ, u) rl (b, v) ⇔ (σ, u) rl (b, v) (you can interchange any member of the class by any other in the matrix)
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 21 / 27 ⊲⊲ |
⇒ ∀(u, v) ∈ H, (au) rl (bv) Lemma (separator): ∀a, b ∈ H, a ⊥ b ⇐ ⇒ ∃ ρ ∈ V
→ z)∩(b − → z) . (⊥⇐ ⇒ ∃ ρ separator) Theorem: ⊥ is an equivalence relation
(under some assumptions)
Theorem (representativity): C equivalence class under ⊥
(under some assumptions)
∀ρ, σ ∈ C, ∀b, u, v ∈ H, (ρ, u) rl (b, v) ⇔ (σ, u) rl (b, v) (you can interchange any member of the class by any other in the matrix)
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 21 / 27 ⊲⊲ |
⇒ ∀(u, v) ∈ H, (au) rl (bv) Lemma (separator): ∀a, b ∈ H, a ⊥ b ⇐ ⇒ ∃ ρ ∈ V
→ z)∩(b − → z) . (⊥⇐ ⇒ ∃ ρ separator) Theorem: ⊥ is an equivalence relation
(under some assumptions)
Theorem (representativity): C equivalence class under ⊥
(under some assumptions)
∀ρ, σ ∈ C, ∀b, u, v ∈ H, (ρ, u) rl (b, v) ⇔ (σ, u) rl (b, v) (you can interchange any member of the class by any other in the matrix)
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 21 / 27 ⊲⊲ |
Equivalence class ⇒ greedy algorithm eating the leaves
A C D E F G H I B A B C D E F G H I
Theorem: When |Cinf| = 1, the graph built is a solution. Theorem: If a tree being a solution exists, |Cinf| = 1. Remark: The graph built is optimal (wrt |V | since V = H) Theorem: When I contains no interferences, the clique of Ci is a valid solution. Remark: It is also optimal
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 22 / 27 ⊲⊲ |
Equivalence class ⇒ greedy algorithm eating the leaves
A C D E F G H I B B D G H I F E C A
Theorem: When |Cinf| = 1, the graph built is a solution. Theorem: If a tree being a solution exists, |Cinf| = 1. Remark: The graph built is optimal (wrt |V | since V = H) Theorem: When I contains no interferences, the clique of Ci is a valid solution. Remark: It is also optimal
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 22 / 27 ⊲⊲ |
Equivalence class ⇒ greedy algorithm eating the leaves
A C D E F G H I B B D G H I F E C A
Theorem: When |Cinf| = 1, the graph built is a solution. Theorem: If a tree being a solution exists, |Cinf| = 1. Remark: The graph built is optimal (wrt |V | since V = H) Theorem: When I contains no interferences, the clique of Ci is a valid solution. Remark: It is also optimal
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 22 / 27 ⊲⊲ |
Equivalence class ⇒ greedy algorithm eating the leaves
A C D E F G H I B D G B H I F E C A
Theorem: When |Cinf| = 1, the graph built is a solution. Theorem: If a tree being a solution exists, |Cinf| = 1. Remark: The graph built is optimal (wrt |V | since V = H) Theorem: When I contains no interferences, the clique of Ci is a valid solution. Remark: It is also optimal
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 22 / 27 ⊲⊲ |
Equivalence class ⇒ greedy algorithm eating the leaves
A C D E F G H I B D G B H I F E C A
Theorem: When |Cinf| = 1, the graph built is a solution. Theorem: If a tree being a solution exists, |Cinf| = 1. Remark: The graph built is optimal (wrt |V | since V = H) Theorem: When I contains no interferences, the clique of Ci is a valid solution. Remark: It is also optimal
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 22 / 27 ⊲⊲ |
Equivalence class ⇒ greedy algorithm eating the leaves
A C D E F G H I B D G B H I F E C A
Theorem: When |Cinf| = 1, the graph built is a solution. Theorem: If a tree being a solution exists, |Cinf| = 1. Remark: The graph built is optimal (wrt |V | since V = H) Theorem: When I contains no interferences, the clique of Ci is a valid solution. Remark: It is also optimal
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 22 / 27 ⊲⊲ |
Let a, b be the elements of Ci with the more interferences. Lemma: no solution with ∃z ∈ H so that z ∈ (a − → b) ⇒ Cut between a and b!
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 23 / 27 ⊲⊲ |
Let a, b be the elements of Ci with the more interferences. Lemma: no solution with ∃z ∈ H so that z ∈ (a − → b) ⇒ Cut between a and b!
α β
Finding out how to cut
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 23 / 27 ⊲⊲ |
Let a, b be the elements of Ci with the more interferences. Lemma: no solution with ∃z ∈ H so that z ∈ (a − → b) ⇒ Cut between a and b!
I1 I2 I3
α β
Finding out how to cut
8 > > > > > < > > > > > : I1 = ˘ u ∈ Ci : a ∈ (b − → u) and b ∈ (a − → u) ¯ I2 = ˘ u ∈ Ci : a ∈ (b − → u) and b ∈ (a − → u) ¯ I3 = ˘ u ∈ Ci : a ∈ (b − → u) and b ∈ (a − → u) ¯ I4 = ˘ u ∈ Ci : a ∈ (b − → u) and b ∈ (a − → u) ¯
I4 = {a; b}
the contrary would imply
a b u
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 23 / 27 ⊲⊲ |
Let a, b be the elements of Ci with the more interferences. Lemma: no solution with ∃z ∈ H so that z ∈ (a − → b) ⇒ Cut between a and b!
I1 I2 I3
α β
Finding out how to cut
8 > > > > > < > > > > > : I1 = ˘ u ∈ Ci : a ∈ (b − → u) and b ∈ (a − → u) ¯ I2 = ˘ u ∈ Ci : a ∈ (b − → u) and b ∈ (a − → u) ¯ I3 = ˘ u ∈ Ci : a ∈ (b − → u) and b ∈ (a − → u) ¯ I4 = ˘ u ∈ Ci : a ∈ (b − → u) and b ∈ (a − → u) ¯
b α β a b α β a
u
v
I2 I3 I1
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 23 / 27 ⊲⊲ |
Let a, b be the elements of Ci with the more interferences. Lemma: no solution with ∃z ∈ H so that z ∈ (a − → b) ⇒ Cut between a and b!
I1 I2 I3
α β
Finding out how to cut
8 > > > > > < > > > > > : I1 = ˘ u ∈ Ci : a ∈ (b − → u) and b ∈ (a − → u) ¯ I2 = ˘ u ∈ Ci : a ∈ (b − → u) and b ∈ (a − → u) ¯ I3 = ˘ u ∈ Ci : a ∈ (b − → u) and b ∈ (a − → u) ¯ I4 = ˘ u ∈ Ci : a ∈ (b − → u) and b ∈ (a − → u) ¯
b α β a b α β a
u
v
I2 I3 I1
Topological sort on the graph associated to the matrix slice gives I1, I2, I3
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 23 / 27 ⊲⊲ |
Let a, b be the elements of Ci with the more interferences. Lemma: no solution with ∃z ∈ H so that z ∈ (a − → b) ⇒ Cut between a and b!
I1 I2 I3
Finding out how to cut How to connect parts afterward First step on I1 → Finds 2 classes I1a and I1α; a ∈ I1a. First step on I3 → Finds 2 classes I1b and I1β; b ∈ I1b.
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 23 / 27 ⊲⊲ |
Let a, b be the elements of Ci with the more interferences. Lemma: no solution with ∃z ∈ H so that z ∈ (a − → b) ⇒ Cut between a and b!
I1 I2 I3
Finding out how to cut How to connect parts afterward First step on I1 → Finds 2 classes I1a and I1α; a ∈ I1a. First step on I3 → Finds 2 classes I1b and I1β; b ∈ I1b. Reconnect I1a and I1b ; Reconnect I1α and I1β.
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 23 / 27 ⊲⊲ |
Let a, b be the elements of Ci with the more interferences. Lemma: no solution with ∃z ∈ H so that z ∈ (a − → b) ⇒ Cut between a and b!
I1 I2 I3
Finding out how to cut How to connect parts afterward First step on I1 → Finds 2 classes I1a and I1α; a ∈ I1a. First step on I3 → Finds 2 classes I1b and I1β; b ∈ I1b. Reconnect I1a and I1b ; Reconnect I1α and I1β. No demonstration of this...
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 23 / 27 ⊲⊲ |
Interference measurement between each pair of hosts.
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 24 / 27 ⊲⊲ |
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 25 / 27 ⊲⊲ |
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 25 / 27 ⊲⊲ |
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 25 / 27 ⊲⊲ |
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 26 / 27 ⊲⊲ |
NWS: System availability
Contributions: – Lower latency – Better responsiveness – Process management Future work: – Automatic deployment
FAST: Routine needs
Contributions: – Generic benchmarking framework – Unified interface to quantitative data – Virtual booking – Integration: DIET, NetSolve, Grid-TLSE – 2 journals; 3 conferences/workshops Future work: – Integration of Freddy – Irregular routines (sparse algebra) – New metrics (like I/O)? – Yet better integration within NWS
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 26 / 27 ⊲⊲ |
NWS: System availability
Contributions: – Lower latency – Better responsiveness – Process management Future work: – Automatic deployment
FAST: Routine needs
Contributions: – Generic benchmarking framework – Unified interface to quantitative data – Virtual booking – Integration: DIET, NetSolve, Grid-TLSE – 2 journals; 3 conferences/workshops Future work: – Integration of Freddy – Irregular routines (sparse algebra) – New metrics (like I/O)? – Yet better integration within NWS
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 26 / 27 ⊲⊲ |
NWS: System availability
Contributions: – Lower latency – Better responsiveness – Process management Future work: – Automatic deployment
FAST: Routine needs
Contributions: – Generic benchmarking framework – Unified interface to quantitative data – Virtual booking – Integration: DIET, NetSolve, Grid-TLSE – 2 journals; 3 conferences/workshops Future work: – Integration of Freddy – Irregular routines (sparse algebra) – New metrics (like I/O)? – Yet better integration within NWS
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 26 / 27 ⊲⊲ |
ALNeM: Network topology to know about interferences
Contributions: – Strong mathematical basements – Optimal in size for cliques of trees – Partial cycle handling – GRAS: application development tool – Submitted to one workshop Future work: – Proof of NP-hardness . . . – . . . or exact algorithm – Experimentation on real platform – Optimization of the measurements – Iterative algo. (modification detection) – Integration within NWS – Hosting of DIET
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 26 / 27 ⊲⊲ |
Book chapter: 1 national
hiérarchique des serveurs de calculs, in Calcul réparti à grande échelle. Hermès Science Paris,
Journals: 2 internationals (+ 1 submitted), 1 national
for Network Enabled Servers. Parallel Computing, special issue on Cluters and Computational Grids for scientific computing, 2003.
Conferences/workshops: 4 internationals (+ 2 submitted), 2 nationals.
Springer-Verlag, Jan 2002.
Parallel and Distributed Systems (PMEO-PDS’02), April 15-19 2002.
Network View. Submitted to Workshop on Grid Benchmarking, associated to IPDPS’04.
Parallel and Distributed Systems: Testing and Debugging, associated to IPDPS’04.
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 27 / 27 ⊲⊲ |
C B A Test Test
NWS NWS
?
bp(AC) = min (bp(AB); bp(BC)) lat(AC) = lat(AB) + lat(BC) It’s a must to reassemble measurements in hierarchical monitoring
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 28 / 27 ⊲⊲ |
A simple idea: Implement the RPC model over the Grid
C C C C C S S S S S
Agent
Client Server Agent Monitor Database
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 29 / 27 ⊲⊲ |
A simple idea: Implement the RPC model over the Grid
C C C C C S S S S S
Agent
Client Several user interfaces which submit the requests to servers Server Agent Monitor Database
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 29 / 27 ⊲⊲ |
A simple idea: Implement the RPC model over the Grid
C C C C C S S S S S
Agent
Client Several user interfaces which submit the requests to servers Server Runs software modules to solve client’s requests Agent Monitor Database
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 29 / 27 ⊲⊲ |
A simple idea: Implement the RPC model over the Grid
C C C C C S S S S S
Agent
Client Several user interfaces which submit the requests to servers Server Runs software modules to solve client’s requests Agent Gets client’s requests and schedules them onto the servers Monitor Database
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 29 / 27 ⊲⊲ |
A simple idea: Implement the RPC model over the Grid
C C C C C S S S S S
Agent
Client Several user interfaces which submit the requests to servers Server Runs software modules to solve client’s requests Agent Gets client’s requests and schedules them onto the servers Monitor Monitors the current state of the resources Database
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 29 / 27 ⊲⊲ |
A simple idea: Implement the RPC model over the Grid
DB
C C C C C S S S S S
Agent
Client Several user interfaces which submit the requests to servers Server Runs software modules to solve client’s requests Agent Gets client’s requests and schedules them onto the servers Monitor Monitors the current state of the resources Database Contains static and dynamic knowledges about resources
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 29 / 27 ⊲⊲ |
A simple idea: Implement the RPC model over the Grid
DB
C C C C C S S S S S
Agent
Client Several user interfaces which submit the requests to servers Server Runs software modules to solve client’s requests Agent Gets client’s requests and schedules them onto the servers Monitor Monitors the current state of the resources Database Contains static and dynamic knowledges about resources
Knowing the platform is crucial for the agent
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 29 / 27 ⊲⊲ |
Temps pdgemm(M, N, K) = K R
p + (K × N)τ p q +
p + λp q
K R
B A Gb Ga Gv2 Gv1 Distributions Matrices grids Possible virtual
5 10 15 20 25 30 35 40 45 50 Ga Gb Gv1 Gv2 Multiplication Redistribution
meas. meas. meas. meas. fore. fore. fore. fore.
de machines parallèles. PhD thesis, 2002.
Algebra Routines for Network Enabled Servers. Parallel Computing, special issue
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 30 / 27 ⊲⊲ |
Error handling Bandwidth test Linux SimGrid TCP SimGrid Syscalls virtualization Conditional execution
Constitutes a portability layer
Grounding features Communications Logs control Leader election Reality Simulation Locks Logs File Host management Data structures Configuration Data Representation Messages and callbacks
Simulates execution span Virtualizes expensive code
Build-in modules Solaris
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 31 / 27 ⊲⊲ |
Hypothesis 1: Routing consistent
A B C Hypothesis 2: Routing symmetric
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 32 / 27 ⊲⊲ |
Ci+1 ← {l1, . . . , lp}
∀hj ∈ Ci, ∀v ∈ hj, do Ei+1 ← Ei+1 ∪ {(v, lj)} and Vi+1 ← Vi+1 ∪ {v}
Let lα, lβ, lγ, lδ ∈ Ci+1 represent respectively hα, hβ, hγ, hδ. For each mα, mβ, mγ, mδ ∈ Ci so that mα ∈ hα, mβ ∈ hβ, mγ ∈ hγ, mδ ∈ hδ. I(Ci+1, )
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 33 / 27 ⊲⊲ |
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 34 / 27 ⊲⊲ |
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 34 / 27 ⊲⊲ |
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 34 / 27 ⊲⊲ |
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 34 / 27 ⊲⊲ |
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 34 / 27 ⊲⊲ |
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 34 / 27 ⊲⊲ |
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 34 / 27 ⊲⊲ |
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 34 / 27 ⊲⊲ |
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 34 / 27 ⊲⊲ |
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 34 / 27 ⊲⊲ |
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 34 / 27 ⊲⊲ |
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 34 / 27 ⊲⊲ |
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 34 / 27 ⊲⊲ |
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 34 / 27 ⊲⊲ |
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 34 / 27 ⊲⊲ |
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 34 / 27 ⊲⊲ |
Goal : Metacomputing platform (GridRPC model)
Main functionalities :
Teams : GRAAL (ENS-Lyon), U. Besançon, Insa-Lyon, Loria (Nancy), Sun. Targeted applications : Grid-ASP
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 35 / 27 ⊲⊲ |
MA
LA LA LA
S S S S S
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 36 / 27 ⊲⊲ |
?
C
MA
LA LA LA
S S S S S
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 36 / 27 ⊲⊲ |
? ? ? ? ? ?
C
MA
LA LA LA
S S S S S
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 36 / 27 ⊲⊲ |
C
MA
LA LA LA
S S S S S
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 36 / 27 ⊲⊲ |
1
S =54
3
S =120 S =5
5
C
1 2 3 4 5
MA
LA LA LA
S S S S S
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 36 / 27 ⊲⊲ |
1
S =54 S =5
5 1
S =54
3
S =120 S =5
5
C
1 2 3 4 5
MA
LA LA LA
S S S S S
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 36 / 27 ⊲⊲ |
S =5
5 1
S =54 S =5
5 1
S =54
3
S =120 S =5
5
C
1 2 3 4 5
MA
LA LA LA
S S S S S
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 36 / 27 ⊲⊲ |
C
MA
MA
MA MA
MA
MA
LA LA LA
S S S S S
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 36 / 27 ⊲⊲ |
S
5
C
MA
MA
MA MA
MA
1 2 3 4 5
MA
LA LA LA
S S S S S
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 36 / 27 ⊲⊲ |
C
MA
MA
MA MA
MA
1 2 3 4 5
MA
LA LA LA
S S S S S
Martin QUINSON December 11th 2003 | ⊳⊳ Slide 36 / 27 ⊲⊲ |